Question

Find the volume (in ${cm}^3$) of this right triangular prism.

• A. $60$
• B. $90$
• C. $120$
• D. $150$

Answer 1

The correct option is A $60$

In the given prism, bases are right-angled triangle.

Let $ac$ be sides and $b$ be hypotenuse of the triangle.

$a=5,c=8$

$\therefore$ By Pythagoras theorem,

$b^2=a^2+c^2$

$=25+64$

$⟹b=\sqrt{89}$

Volume of triangular prism $=\frac{3}{4}\sqrt{-a^4+2(ab{)}^2+2(ac{)}^2-b^4+2(bc{)}^2-c^4}$

$=\frac{3}{4}\sqrt{-(a^4+b^4+c^4)+2\left(\right(ab{)}^2+(ac{)}^2+(bc{)}^2)}$

$=\frac{3}{4}\sqrt{-12642+19042}$

$=\frac{3}{4}\times 80=60$

Hence, Volume of triangular prism is $60c{m}^3$.